The Fixed Point Theorems For Several Nonlinear Operators And Their Applications

In this paper, we mainly study the existence of the fixed points of mixed monotone operatorsand set-valued increasing operators. We also study the solutions of nonlinear integro-diferentialequation of mixed type in Banach space where the integral kernel is boundless. The paper isconstituted with four chapters.In chapter one, we introduce the background and main results about nonlinear operators andnonlinear integro-diferential equations. Besides, we also simply illustrate how and why this topicscomes out.In chapter two, we present the existence of some fixed points and coupled minimal-maximalfixed points of compound mixed monotone operators in partial ordered sets and partially orderedtopological spaces. We improve some already existing results.In chapter three, we consider two kinds of set-valued increasing operators in partially Banachspaces and partially ordered topological spaces respectively. We obtain three fixed point theorems.In chapter four, we discuss the existence of maximal and minimal solutions, the iterativeapproximation of solutions of the initial value problem for nonlinear integro-diferential equationsof mixed type in Banach spaces. We generalize and improve the corresponding results in somepapers.